Statistics homework help.

Statistics (Math 141)

# Homework: B3

## Instructions

Please complete all problems. Unless otherwise noted, each problem is worth 5 points. To obtain full credit, you must use the methods specified in the course text. *Please*, format your work as explained in chapter 2 of the Frequently Asked Questions (FAQ) document. When doing calculations, such as the variance, standard deviation, or the correlation coefficient, use technology wherever possible. There is no need to do calculations by hand unless I direct you to do so. You can find suggestions for doing charts in chapter 5 of the FAQ document. When graphing by hand, remember to use graph paper. Round all calculations to three decimal places.

**Allow time.** In this assignment, you will begin to study probability, a topic that is difficult for many students. The concepts you learn will be used again and again for the remainder of the course. For this reason, you should allow adequate time to complete this assignment.

## Assignment Problems

### Section 9.1

**True or False?**A correlation coefficient, r=−0.8r=−0.8, represents a linear correlation that is less strong than when r=0.8r=0.8.- Using the scatter plot in Figure 1, state whether there is a positive linear correlation, negative linear correlation, or no linear correlation between the variables.

**Problems 3-5** Use the data sets in Table 1 to answer the questions.

Crimes, xx | 1.60 | 1.55 | 1.44 | 1.40 | 1.32 | 1.23 | 1.22 |
---|---|---|---|---|---|---|---|

Arrests,yy | 0.78 | 0.80 | 0.73 | 0.72 | 0.68 | 0.64 | 0.63 |

Crimes, xx | 1.23 | 1.22 | 1.18 | 1.16 | 1.19 | 1.21 | 1.20 |

Arrests,yy | 0.63 | 0.62 | 0.60 | 0.59 | 0.60 | 0.61 | 0.58 |

- Display the data in a scatter plot. (
*Please*, orient the x and y-axes in the usual way.) - Calculate the correlation coefficient, rr (Note: use technology for the calculation).
- What do you conclude about the type of correlation?

### Section 9.2

- When are predictions made using a regression line meaningful?
- If the correlation between xx and yy is
*not*significant, what is the best value to use when predicting yy?

**Problems 8-11.** Use the data in Table 2 to answer the questions.

xx | 37 | 39 | 43 | 45 | 41 | 47 |
---|---|---|---|---|---|---|

yy | 76 | 82 | 77 | 59 | 91 | 56 |

- What is the equation of the regression line?
- Construct a scatter plot for the data showing the regression line
*and*the data points on the same graph.

**Problems 10-11.** Use the regression equation found in question 9 to predict the value of yy for the values of xx given. If it is not meaningful to predict the value of yy, explain why not.

- x=40x=40
- x=25x=25

### Section 3.1

**Problems 12-13.** Answer the following questions. A probability experiment is conducted by first spinning the spinner shown in Figure 2, then tossing a coin.

- What set represents the sample space (Note: show all elements of the sample space using set notation.)
- Draw a tree diagram for the probability experiment.
**Multiple Choice Quiz.**A multiple choice quiz has five possible answers per question. Assuming that no questions are left unanswered, in how many ways can an 8 question multiple choice quiz be answered?**True or False?**A probability of 0.08 is considered unusual.**True or False?**A probability always lies in the interval [0,1][0,1] on the real number line.**Probability Experiment**. A probability experiment consists of spinning the spinner (*Note*: The spinner is the same one specified for problems 12 and 13.) and rolling a six-sided die. What is the probability of spinning an even number and then rolling an odd number greater than 2? (*Note*: you can assume an equal probability for all numbers on the spinner and the die toss.)- Use the frequency distribution in Table 3. Find the probability that a voter chosen at random is between 35 and 64 years old?.

Ages of Voters | Frequency (in millions) |
---|---|

18 to 20 years old | 6.4 |

21 to 24 years old | 7.6 |

25 to 34 years old | 22.3 |

35 to 44 years old | 29.4 |

45 to 64 years old | 57.2 |

65 years old and over | 28.5 |

- Use the pie chart in Figure 3 to find the probability that a student attained less than B on the quiz?

### Section 3.2

**Classifying Events.**A ball numbered 1 though 52 is selected from a bin, replaced, and then a second ball is selected from the bin. Are the events independent or dependent?

**Problems 21-25.**Use the information in Table 4 to answer the questions.

Nursing Majors |
Non-Nursing Majors |
Total | |
---|---|---|---|

Males | 203 | 1305 | 1508 |

Females | 841 | 1498 | 2339 |

Total | 1044 | 2803 | 3847 |

- Find the probability that a randomly selected student is a nursing major.
- Find the probability that a randomly selected student is female.
- Find the probability that a randomly selected student is a nursing major given that the student is a female.
- Find the probability that a randomly selected student is a nursing major and male.
- Are the events being a male student and being a nursing major independent or dependent events? Show the probability calculations that support your answer.